ASEI Lesson Plan on Physics

Subject: Physics

Theme: Waves

Topic: Wave Motion

Sub Topic: Wave Motion

Date: dd/mm/yyyy

Class: S.S.S 2

Duration: 50 Minutes

No of Learners: 30

Learning Objectives:

1. Identify and Define a wave.

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1. A wave transfers energy from one place to another without the transfer of particles in the medium. Rather, individual particles vibrate (oscillate) at fixed positions instead.
2. A wave is a disturbance which travels outward from its source, carrying energy along with it.
3. Wave motion can also be defined as a process of transferring disturbance (in form of kinetic energy) from one point to another in a medium without any transfer of particles of the medium.
4. Wave motion can be defined as a disturbance which travels through a medium transferring energy from one point to another without causing any permanent displacement of the medium.

2. Explain Mechanical waves and Electromagnetic waves.

   1. Mechanical waves are those waves that require a material medium for their propagation.
      Examples of such waves are water waves, sound waves, and waves on a rope or string.
   2. Electromagnetic waves are waves that do not require a material medium for propagation. Examples are light waves, radio waves, X-rays and gamma rays.

3. Explain Stationary waves, progressive waves and the types of progressive (travelling) waves.

   1. Stationary wave:

      Waves which appear to be vibrating vertically without travelling horizontally created from waves with identical frequency and amplitude interfering with one another while travelling in opposite directions.
      Examples of standing waves are; waves generated by piano, guitar string, two people shaking a jump rope, etc.

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   2. Progressive Wave:

      A wave which continues to spread out transferring energy from the source of disturbance is called a progressive wave.
      Progressive waves have properties such as wavelength, height, amplitude, velocity, frequency, and period. Examples of progressive waves are sound waves, seismic waves, and water waves.

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   There are two types of progressive waves.

   1. Transverse waves: are waves which travel perpendicularly to the direction of the vibrations producing the waves. That is, a transverse wave is one in which the particle displacements are perpendicular to the direction along which the wave travels. The water wave is a transverse wave since the up-and-down (vertical) motion of the water particles is perpendicular to the direction of wave propagation (horizontal, along the wave surface). Other examples are; light waves, radio waves and wave produced in a rope.

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   2. A longitudinal wave: is one in which the particle displacements are parallel to the direction along which the wave travels. That is, longitudinal waves are waves which travel in a direction parallel to the vibrations of the medium. The sound wave is an example of a longitudinal wave.

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4. Explain the graphic representation of a wave.

Both transverse and longitudinal waves are represented by a sine curve.

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5. Explain the terms used in describing a wave.

   The dots on the graph represent the positions of the particles at that instant and the arrows indicate the direction of motion of these particles.

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   1. Phase: Particles which are at the same verticle distances from their positions of rest and are moving in the same direction are said to be in the same phase. Particles A, C and E are in phase.
   2. A Cycle: is a complete to-and-fro movement or direction of a vibrating particle.
   3. Crest: This is the highest point on the wave.
   4. Trough: This is the lowest point on the wave.
   5. A Node: A node is a point on a stationary wave where there is no movement of the medium. That is a point at which the amplitude of vibration in the standing wave system is zero. The nodes are λ/2 apart.
   6. An antinode: Is a point on a stationary wave where there is the maximum displacement of the medium. Antinodes are λ/2 apart.
   7. Amplitude (A): This is the maximum displacement of a particle from its resting position. It is measured in metres.
   8. Wavelength (λ): This is the distance between two successive crests or successive troughs (or two successive points in phase) of the wave. It is measured in metres.
   9. Wavefronts: Can be represented as lines which are always perpendicular to the direction of wave travel. The distance between one wavefront to the next is the wavelength.
   10. Frequency (f):This is the number of complete vibrations or cycles that a particle makes in one second. It is also equivalent to the number of complete waves passing at a given point in one second. The S.I unit of frequency is the Hertz (Hz) which is defined as one cycle or oscillation per second (1 cps).
       The frequency of a wave is identical to the frequency of the source that sends it out.
   11. Period (T): This is the time taken by a wave-particle to make one complete oscillation. It is measured in seconds. The period is also the time taken by the wave to travel one wavelength.
       

       The period (T) and frequency (f) are related by
       f = 1/T or
       T = 1/f

   12. Wave Speed or velocity (v): This is the distance the wave travels in one second. Its unit is metre-per-second (m/s)

6. Write and express the Mathematical Relationships between Frequency (f), Wavelength (λ) and Velocity (v).

   Velocity = Frequency x Wavelength
   v = fλ ----------- (1)
   But f = 1/T
   Hence v = λ/T
   λ = vT ----------- (2)

7. Write the Mathematical Representation of Wave Motion - Progressive Wave.

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8. List and explain the properties of waves:

   The properties of waves include; Reflection, Refraction, Interference, Diffraction, and Polarization.

   1. Reflection of waves:

   Waves are reflected upon encountering a barrier. If the barrier is plane, the angle of incidence is equal to the angle of reflection. The frequency, speed and wavelength of the waves remain unchanged as long as they remain in the same medium after reflection.
   Law of Reflection: When a wave strikes an interface, the angle of incidence measured to the normal of the interface is equal to the angle of reflection.

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   2. Refraction of wave:

   Refraction is the change in the speed and direction of the waves as they cross the boundary between two media of different densities.
   The wave travels more slowly in shallow water compared to deep water.
   The angle of incidence (i) is the angle the direction of the incident wavefront makes with the normal at the boundary surface. The angle of refraction (r) is the angle the direction of the refracted ray makes with the normal to the plane boundary.
   N/B. The wavelength decreases and the direction shift as the wave hit the more shallow side.

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   N/B. The amount by which a wave is refracted by a material is given by the refractive index of the material. The directions of incidence and refraction are related to the refractive indices of the two materials by Snell's law.
   

   3. Diffraction of wave:

   Diffraction is the ability of waves to bend around obstacles in their path. A wave exhibits diffraction when it encounters an obstacle that bends the wave or when it spreads after emerging from an opening. The amount of diffraction depends on the wavelength of the wave compared with the size of the gap. That is, Diffraction effects are more pronounced when the size of the obstacle or opening is comparable to the wavelength of the wave.

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   4. Interference of wave:

      When two or more waves meet, they interact with each other. The interaction of waves with other waves is called wave interference.Wave interference may occur when two waves that are traveling in opposite directions meet.Interference is the effect produced when two waves of the same frequency, amplitude and wavelength traveling in the same direction in a medium are superposed - as they simultaneously pass through a given point. The two waves pass through each other, and this affects the amplitude. How amplitude is affected by wave interference depends on the type of interference. Interference can be constructive or destructive.
      1. Constructive Interference:
      Constructive interference occurs when the crests of one wave overlap the crests of the other wave. As the waves pass through each other, the crests combine to produce a wave with greater amplitude.
      

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      2. Destructive Interference:
      Destructive interference occurs when the crests of one wave overlap the trough of another wave. As the waves pass through each other, the crests and troughs cancel each other out to produce a wave with zero amplitude.

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      The task of determining the shape of the resultant demands that the principle of superposition is applied. The principle of superposition is sometimes stated as follows:

      When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.

      Displacement of Pulse A	Displacement of Pulse B	Resulting Displacement	Displacement of Pulse A and B = Resulting Displacement
      +1	+1	+2
      -1	-1	-2
      +1	-1	0
      +1	-2	-1
      +2	-1	+1

   5. Polarization of Wave:

   A light wave that is vibrating in more than one plane is referred to as unpolarized light. Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light. Such light waves are created by electric charges that vibrate in a variety of directions, thus creating an electromagnetic wave that vibrates in a variety of directions.
   In general, it is helpful to picture unpolarized light as a wave that has an average of half its vibrations in a horizontal plane and half of its vibrations in a vertical plane.
   
   

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   It is possible to transform unpolarized light into polarized light. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization.
   
   1. Types of Polarization:
      • Linear Polarization:
      In linear polarization, the electric field of light is limited to a single plane along the direction of propagation.
      • Circular Polarization:
      There are two linear components in the electric field of light that are perpendicular to each other such that their amplitudes are equal, but the phase difference is ∏/2.
      The propagation of the occurring electric field will be in a circular motion.
      • Elliptical Polarization:
      The electric field of light follows an elliptical propagation. The amplitude and phase differences between the two linear components are not equal.
   
   

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9. List methods Used in the Polarization of Light

   1. Polarization by Transmission
   2. Polarization by Reflection
   3. Polarization by Scattering
   4. Polarization by Refraction

10. Explain Applications of Polarization.

    1. Polarization is used in sunglasses to reduce glare.
    2. Polaroid filters are used in plastic industries for performing stress analysis tests.
    3. Three-dimensional movies are produced and shown with the help of polarization.
    4. Polarization is used for differentiating between transverse and longitudinal waves.
    5. Infrared spectroscopy uses polarization.
    6. It is used in seismology to study earthquakes.
    7. In Chemistry, the chirality of organic compounds is tested using polarization techniques.

11. Solve problems on a wave.

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Rationale:

Waves are everywhere. Whether we recognize it or not, we encounter waves daily. Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, cosine waves, stadium waves, earthquake waves, waves on a string, and slinky waves are just a few examples of our daily encounters with waves. waves play a significant role in life because they transfer energy and waves allow for long-range communication via mobile phones, television and radio. sound is waves, pressure waves that travel in air or other fluids or solids. We use sound to hear things, to communicate, and ultrasound (sound too high a frequency to hear) to diagnose illnesses, or to look inside solid materials for flaws, and probably a lot more things. Then there are electromagnetic waves, which are used for radio broadcasting and communications, cellphones, RF remote controls, measuring distances and location (GPS), and even for learning about space by analyzing radio frequency waves coming from galaxies and stars. XRays are radio waves that are just a lot higher frequency. They are called 'ionizing radiation' because they can strip electrons from individual atoms. Light is also a wave (or a particle, depending on how you're talking about it). Light is an electromagnetic wave, like radio waves and X-rays but even higher frequency. Without light, we couldn't see. Also, all the energy that comes to earth is light from the sun, which plants use to make oxygen for us to breathe and food for us to eat. Also, lasers are used for millions of things these days, from surgery to welding metal and plastic, for measuring, communications, targetting munitions, etc. Then there are ocean waves. Useful for surfing.

Prerequisite/ Previous knowledge:

• Newton's Law of Motion
• Physical Wave

Learning Materials:

Reference Materials:

• New School Physic for Senior Secondary Schools, by M. W. Anyakowa.
• Lamlas's SSCE and UTME, by O. Ajaja and H. B. Olaniyi

Lesson Development: